phase noise tolerant modulation formats and dsp...

Phase Noise Tolerant Modulation Formats and DSP

Algorithms for Coherent Optical Systems

JAIME RODRIGO NAVARRO

Doctoral Thesis in Physics

School of Engineering Sciences

KTH Royal Institute of Technology

Stockholm, Sweden

June 2017

TRITA-FYS 2017:30 KTH Royal Institute of Technology

ISSN 0280-316X School of Engineering Sciences

ISRN KTH/FYS/--17:30—SE SE-164 40 Stockholm

ISBN: 978-91-7729-424-5 SWEDEN

Akademisk avhandling som med tillstånd av Kungl Tekniska Högskolan framlägges till offentlig

granskning för avläggande av teknologie doktorsexamen i fysik fredagen den 9 juni 2017 klockan

10.00, i Sal C, Electrum, Kungl Tekniska Högskolan Kistagågen 16, Kista.

© Jaime Rodrigo Navarro, June 2017

Tryck: Universitetsservice US-AB

iii

Abstract

Coherent detection together with multilevel modulation formats has the potential to significantly

increase the capacity of existing optical communication systems at no extra cost in signal bandwidth.

However, these modulation formats are more susceptible to the impact of different noise sources and

distortions as the distance between its constellation points in the complex plane reduces with the

modulation index. In this context, digital signal processing (DSP) plays a key role as it allows

compensating for the impairments occurring during signal generation, transmission and/or detection

relaxing the complexity of the overall system. The transition towards pluggable optical transceivers,

offers flexibility for network design/upgrade but sets strict requirements on the power consumption

of the DSP thus limiting its complexity. The DSP module complexity however, scales with the

modulation order and, in this scenario, low complex yet high performance DSP algorithms are highly

desired.

In this thesis, we mainly focus on the impact of laser phase noise arising from the transmitter and

local oscillator (LO) lasers in coherent optical communication systems employing high order

modulation formats. In these systems, the phase noise of the transmitting and LO lasers translate into

phase noise in the received constellation impeding the proper recovery of the transmitted data. In

order to increase the system phase noise tolerance, we firstly explore the possibility of re-arranging

the constellation points in a circularly shaped mQAM (C-mQAM) constellation shape to exploit its

inherent phase noise tolerance. Different low-complex carrier phase recovery (CPR) schemes

applicable to these constellations are proposed along with a discussion on its performance and

implementation complexity. Secondly, the design guidelines of high performance and low complex

CPR schemes for conventional square mQAM constellations are presented. We identify the inherent

limitation of the state-of-the-art blind phase search (BPS) carrier phase recovery algorithm which

hinders its achievable performance and implementation complexity and present a low complex

solution to overcome it. The design guidelines of multi-stage CPR schemes for high order modulation

formats, where the BPS algorithm is employed at any of the stages, are also provided and discussed.

Finally, the interplay between the received dispersed signal and the LO phase noise is analytically

investigated to characterize the origin of the equalization enhanced phase noise phenomena.

iv

Sammanfattning

Koherent detektion tillsammans med multinivå-modulationsformat kan avsevärt öka kapaciteten hos

befintliga optiska kommunikationssystem utan ökning av signalbandbredden. Dessa

modulationsformat är emellertid mer mottagliga för brus och distorsion, eftersom avståndet mellan

konstellationspunkterna i det komplexa planet minskar med ordningen på modulationsformatet. I

detta sammanhang spelar digital signalbehandling (DSP) en nyckelroll eftersom det möjliggör

kompensering för de störningar som uppstår under signalgenerering, överföring och / eller

detektering, vilket minskar kraven på systemet som helhet. Övergången till pluggbara optiska

transceivers, erbjuder flexibilitet för nätverksdesign / uppgradering, men ställer strikta krav på DSP-

strömförbrukningen, vilket begränsar DSP-algoritmernas möjliga komplexitet. Därför är DSP-

algoritmer för högre ordningens modulationsformat med låg komplexitet men hög prestanda mycket

önskvärda.

I denna avhandling fokuserar vi främst på effekten av det fasbrus som kommer från både sändarlasern

och lokaloscillator-lasern (LO) i koherenta optiska kommunikationssystem som använder högre

ordningens modulationsformat. I dessa system orsakar fasbruset från sändnings- och LO-lasrarna,

fasbrus i den mottagna konstellationen vilket förhindrar att den sända datan korrekt återskapas på

mottagarsidan. För att öka systemets fasbrusstolerans undersöker vi, för det första möjligheten att

rearrangera konstellationspunkterna i en cirkulärformad mQAM (C-mQAM) konstellationsform för

att utnyttja dess inneboende fasbrustolerans. Olika metoder föreslås för fasåtervinning (CPR) för

dessa konstellationer och deras komplexitet och prestanda diskuteras. För det andra presenteras

designregler för högpresterande CPR-system med låg komplexitet för konventionella kvadratiska

mQAM-konstellationer. En inneboende begränsning hos fasåtervinningsalgoritmen Blind Phase

Search (BPS) identifieras vilken begränsar prestandan och ökar implementeringskomplexiteten. En

enkel lösning för att övervinna denna begränsning presenteras. Konstruktionsriktlinjer för flerstegs

CPR-system för högre ordningens modulationsformat, där BPS-algoritmen används i något av stegen,

presenteras och diskuteras. Slutligen undersöks analytiskt samspelet mellan den mottagna signalen

som utsatts för fiberns dispersion och LO-fasbruset för att karakterisera orsaken till det fenomen som

kallas Equalization Enhanced Phase Noise.

v

Acknowledgments

I would like to take this opportunity to express my sincere gratitude to all people who contributed to

this very key moment. I start by thanking my supervisors; Prof. Sergei Popov for his indispensable

guidance and kind help during this journey and for making the process an easy-going task. Prof.

Gunnar Jacobsen for his trust, invaluable guidance and for having the honor of sharing his broad

experience and knowledge which were crucial to the achievements I accomplished. Dr. Richard

Schatz for his enthusiasm, kind help and for sharing his priceless technical knowledge essential to

solve the most difficult obstacles I faced during my PhD studies. Dr. Xiaodan Pang, for his patience

while providing me with the smoothest possible starting process. His profound technical knowledge

was essential and his joyful character made my PhD studies a pleasant journey. Dr. Oskars Ozolins

for keeping me steadily focused. His technical expertise and his strive for excel were essential to

accomplish my achievements. Anders Berntson and the Kista High Speed Transmission Laboratory

team members for giving me the opportunity to develop myself in such an enriching working

atmosphere. I continue thanking Assoc. Prof. Darko Zibar for hosting me and supervising my

research during my stay in DTU. Hadrien Louchet and Andre Richter for their pleasant supervision

while hosting my stay at VPIphotonics.

I continue thanking my office mate and friend Aditya Kakkar for the most productive collaboration

crucial to the achievements made during my PhD studies. Dr. Aleksejs Udalcovs for his kind help,

technical discussions and joyful moments. My colleagues Elena, Sebastian and Miguel from KTH,

Francesco, Molly and Edson from DTU, my friends from ICONE, Ksenia, Auro, Asif, Simone,

Giuseppe, Francesca, Tu, Marti, Faruk, Hugo, Hou-Man as well as the project management members.

I would also like to thank my friends in Stockholm for making my stay here an unforgettable

experience. Not to forget mentioning my life friends from UPV and their support, Thanks.

Y para terminar, quiero dar las gracias al grupo mas importante de todos, mi familia. Especialmente

mi madre Amparo Navarro Puchades, mi padre Jaime Rodrigo Gonzalvo y mi hermana Amparo

Rodrigo Navarro a quienes le debo todo. A pesar de la distancia, su apoyo y amor incondicional han

sido clave para mantenemre firme durante todo este tiempo y conseguir todo lo que me proponga.

Tanto por los que estan como los que ya no, sin vosotros nada de esto hubiese sido remotamente

posible. Muchísimas gracias.

vii

Contents

Acknowledgments ......................................................................................................................... v

Contents ....................................................................................................................................... vii

List of Figures ............................................................................................................................... ix

List of Tables ................................................................................................................................. xi

List of Abbreviations ................................................................................................................... xii

List of Publications ..................................................................................................................... xv

Chapter 1 Introduction ................................................................................................................. 1

1.1 Historical Background........................................................................................................ 1

1.1.1 History of Traditional Direct-Detection Optical Communications ......................... 1

1.1.2 Coherent Optical Communications ......................................................................... 3

1.2 Phase Noise in Coherent Optical Systems ......................................................................... 4

1.3 Overview of the Thesis Contribution ................................................................................. 5

Chapter 2 Coherent Optical Fiber Communication Systems ................................................... 7

2.1 Transmitter ......................................................................................................................... 7

2.1.1 Modulation Formats ................................................................................................ 7

2.1.2 Pulse Shaping Filter ................................................................................................ 9

2.1.3 Dual-nested IQ Mach-Zehnder modulator (IQ MZM) ......................................... 10

2.1.4 Laser sources ......................................................................................................... 10

2.2 Optical Fiber Channel ....................................................................................................... 11

2.2.1 Attenuation in Optical Fibers ................................................................................ 12

2.2.2 Fiber Dispersion .................................................................................................... 13

2.2.3 Polarization Mode Dispersion............................................................................... 14

2.3 Coherent Optical Receiver ............................................................................................... 15

2.3.1 Analog-to-Digital Converters ............................................................................... 16

2.4 Digital Signal Processing ................................................................................................. 16

2.4.1 De-Skew and Orthonormalization ........................................................................ 17

2.4.2 Static Channel Equalization .................................................................................. 17

2.4.3 Interpolation and Timing Recovery ...................................................................... 17

2.4.4 Dynamic Channel Equalization ............................................................................ 18

2.4.5 Frequency Offset Compensation ........................................................................... 19

2.4.6 Carrier Phase Recovery......................................................................................... 20

2.4.7 Symbol Estimation and Decoding ........................................................................ 20

Chapter 3 CPR Schemes for Phase Noise Tolerant Circular mQAM Formats .................. 21

3.1 Phase Noise Tolerant C-mQAM....................................................................................... 21

3.2 Adaptive Boundaries for Cycle slip Mitigation ............................................................... 25

3.3 n-PSK Partitioning algorithm for C-mQAM .................................................................... 26

3.4 Two Stage n-PSK Partitioning CPR Scheme for C-mQAM ............................................ 29

3.4 Experimental validation of the proposed CPR schemes for C-mQAM ........................... 31

viii CONTENTS

Chapter 4 Carrier Phase Recovery Algorithms for Square mQAM ................................... 33

4.1 Efficient blind phase search based carrier phase recovery with angular quantization noise

mitigation ......................................................................................................................... 33

4.2 Multi-stage Carrier Phase Recovery Schemes with Angular Quantization Noise Mitigation

............................................................................................................................. 37

4.2.1 Multi-Stage Carrier Phase Recovery Architecture Design ................................... 37

4.3 Experimental validation of the proposed CPR schemes for Sq-mQAM .......................... 40

Chapter 5 Laser Frequency Noise Impact on Coherent Optical Communications with

Electronic Chromatic Dispersion Compensation ..................................................................... 43

5.1 Equalization enhanced phase noise in dispersion-unmanaged coherent systems employing

lasers with white frequency noise spectrum ..................................................................... 43

5.2 Equalization enhanced phase noise in dispersion-unmanaged coherent systems employing

lasers with general non-white frequency noise spectrum................................................. 48

Chapter 6 Conclusions and Future Research ........................................................................... 51

Chapter 7 Summary of the Original Works ............................................................................. 55

References .................................................................................................................................... 61

ix

List of Figures

Figure 2.1 General structure of a DSP-based optical transmitter ........................................... 8

Figure 2.2 Square 16QAM and circular 16QAM constellations shape .................................. 9

Figure 2.3 Dual-nested Mach-Zender modulator structure .................................................. 10

Figure 2.4 Group delay per unit length. ............................................................................... 14

Figure 2.5 Coherent optical receiver structure with polarization diversity. ......................... 15

Figure 2.6 Ninety degree hybrid transfer function. .............................................................. 15

Figure 2.7 DSP modules in a digital coherent optical receiver. ........................................... 16

Figure 2.8 Adaptive MIMO equalizer structure. .................................................................. 19

Figure 3.1 Viterbi and Viterbi block diagram for CPR. ....................................................... 22

Figure 3.2 Blind phase search block diagram for CPR. ....................................................... 23

Figure 3.3 Circular 16QAM constellation and 64QAM constellations shape .................... 25

Figure 3.4 Block diagram of the proposed adaptive boundaries module ............................. 25

Figure 3.5 OSNR sensitivity penalty versus combined linewidth symbol duration

product for the proposed adaptive boundaries module ....................................... 26

Figure 3.6 Block diagram of the proposed n-PSK partitioning CPR scheme. ..................... 27

Figure 3.7 Distribution of the constellation points in C-16QAM and C-64QAM

constellations along with the proposed bit mapping, differential sector

encoding and symbol amplitude classes. ............................................................ 28


product comparative for the proposed n-PSK partitioning scheme .................... 28

Figure 3.9 Block diagram of the proposed two-stage n-PSK partitioning CPR scheme...... 30

Figure 3.10 Flow chart diagram of the proposed two-stage n-PSK partitioning CPR

scheme for an optimization of its implementation complexity. .......................... 30

Figure 3.11 OSNR sensitivity penalty versus the combined linewidth symbol duration

product for the proposed two-stage n-PSK partitioning CPR scheme ............... 31

Figure 3.12 Experimental performance comparative of the proposed n-PSK partitioning

CPR scheme. ....................................................................................................... 32

Figure 3.13 Experimental performance comparative between different proposed CPR

schemes. .............................................................................................................. 32

x LIST OF FIGURES

Figure 4.1 FN-PSD of different tracked phases by the C-BPS ............................................ 34

Figure 4.2: Block diagram of the proposed F-BPS CPR scheme. ......................................... 35


product comparative between the proposed F-BPS and the C-BPSCPR

schemes. .............................................................................................................. 35

Figure 4.4 Tolerable combined linewidth symbol duration product comparative

between the proposed F-BPS and C-BPS CPR schemes. ................................... 36

Figure 4.5 Block diagram of two different multi-stage CPR design architectures. ............. 37

Figure 4.6 Block diagram of different CPR schemes for the second stage in a multi-

stage CPR.. .......................................................................................................... 38

Figure 4.7 OSNR penalty versus tolerable combined linewidth symbol duration

product performance of the proposed multi-stage CPR schemes ....................... 39

Figure 4.8 Tolerable linewidth symbol duration product versus effective number of test

phases performance of the proposed multi-stge CPR schemes. ......................... 40

Figure 4.9 Experimental performance comparative between the proposed F-BPS and

the C-BPS CPR schemes. ................................................................................... 41

Figure 4.10 Experimental validation of the proposed multi-stage CPR schemes. ................. 41

Figure 5.1 General system model of a coherent optical communication system for

EEPN analysis. .................................................................................................... 44

Figure 5.2 Influence of the LO low frequency noise spectrum on the EEPN

phenomenon. ....................................................................................................... 45

Figure 5.3 Experimental validation of the influence of low frequency noise on EEPN. ..... 46

Figure 5.4 Experimental validation of the proposed mitigation bandwidth design

parameter............................................................................................................. 47

Figure 5.5 Qualitative representation of the EEPN phenomenon. ....................................... 48

Figure 5.6 Regime segmentation of the frequency noise spectrum. .................................... 49

xi

List of Tables

Table 3.1 Computational complexity reduction factors relative to the n-PSK

partitioning CPR scheme .................................................................................... 29

Table 3.2 Computational complexity reduction factors relative to the two-stage

n-PSK partitioning CPR scheme. ........................................................................ 31

Table 4.1 Computational complexity reduction factors relative to the C-BPS of

different proposed CPR schemes ........................................................................ 39

file:///C:/Users/jairod/Desktop/PhD%20Thesis/PHD%20thesis%20CPR%20main%20part/Jaime%20Thesis%20Draft%20Mail33.docx%23_Toc480028667file:///C:/Users/jairod/Desktop/PhD%20Thesis/PHD%20thesis%20CPR%20main%20part/Jaime%20Thesis%20Draft%20Mail33.docx%23_Toc480028667file:///C:/Users/jairod/Desktop/PhD%20Thesis/PHD%20thesis%20CPR%20main%20part/Jaime%20Thesis%20Draft%20Mail33.docx%23_Toc480028669file:///C:/Users/jairod/Desktop/PhD%20Thesis/PHD%20thesis%20CPR%20main%20part/Jaime%20Thesis%20Draft%20Mail33.docx%23_Toc480028669

xii

List of Abbreviations

AGC Automatic gain control

ASIC Application-specific integrated circuit

AWG Arbitary waveform generator

AWGN Additive white Gaussian noise

BER Bit error ratio

BPS Blind phase search

BPSK Binary phase shift keying

C-BPS Conventional blind phase search

CMA Constant modulus algorithm

C-mQAM Circular m-ary quadrature amplitude modulation

CPR Carrier phase recovery

DAC Digital-to-analogue converter

DDPLL Decision-directed phase-locked loop

DSF Dispersion shifted fiber

DSP Digital signal processing

EDFA Erbium doped fiber amplifier

EEPN Equalization enhanced phase noise

F-BPS Filtered blind phase search

FEC Forward error correction

FFT Fast Fourier transform

FIR Finite impulse response

FSR Free spectral range

FWM Four wave mixing

IMDD Intensity-modulation direct-detection

LED Light-emitting diode

LO Local oscillator

MIMO Multiple-input and multiple-output

MLE Maximum likelihood estimator

MMA Multi-modulus algorithm

LIST OF ABBREVIATIONS xiii

mQAM m-ary quadrature amplitude modulation

MZM Mach-Zehnder modulator

OSNR Optical signal to noise ratio

PBC Polarization beam combiner

PMD Polarization mode dispersion

PSK Phase shift keying

QPSK Quadrature phase shift keying

SER Symbol error ratio

SNR Signal to noise ratio

SSMF Standard single mode fiber

V&V Viterbi and Viterbi

xv

List of Publications

Publications included in this thesis:

Paper I:

J. Rodrigo Navarro, X. Pang, A. Kakkar, O. Ozolins, R. Schatz, G. Jacobsen,

S. Popov, "Adaptive Boundaries Scheme for Cycle-Slip Mitigation in C-mQAM

Coherent Systems," IEEE PTL, 27(20), 2154-2157 (2015).

Paper II: J. Rodrigo Navarro, A. Kakkar, X. Pang, O. Ozolins, R. Schatz, M. Iglesias

Olmedo, G Jacobsen, S. Popov, “Carrier Phase Recovery Algorithms for

Coherent Optical Circular mQAM Systems,” IEEE/OSA J. Lightwave Technol.

34(11), 2717-2723 (2016).

Paper III: J. Rodrigo Navarro, A. Kakkar, X. Pang, M. Iglesias Olmedo, O. Ozolins, F.

Da Ros, M. Piels, R. Schatz, D. Zibar, G. Jacobsen, S. Popov, “Two-Stage n-PSK

Partitioning Carrier Phase Recovery Scheme for Circular mQAM Coherent

Optical Systems,” Photonics. 3(2), 37 (2016).

Paper IV: J. Rodrigo Navarro, M. I. Olmedo, A. Kakkar, X. Pang, O. Ozolins, R. Schatz,

G. Jacobsen, S. Popov, D. Zibar, “Phase Noise Tolerant Carrier Recovery

Scheme for 28 Gbaud Circular 16QAM”, in Proc. of ECOC 2015 (OSA/IEEE,

2015), paper Mo.4.3.5.

Paper V: J. Rodrigo Navarro, A. Kakkar, R. Schatz, X. Pang, O. Ozolins, A. Udalcovs,

S. Popov, G. Jacobsen, “Blind phase search with angular quantization noise

mitigation for efficient carrier phase recovery,” MDPI Photonics, to appear.

Paper VI: J. Rodrigo Navarro, A. Kakkar, R. Schatz, X. Pang, O. Ozolins, F. Nordwall,

H. Louchet, S. Popov, G. Jacobsen, “High Performance and Low Complexity

Carrier Phase Recovery Schemes for 64-QAM Coherent Optical Systems,” in

OFC 2017, (OSA, 2017), paper W2A.53.

Paper VII J. Rodrigo Navarro, A. Kakkar, X. Pang, O. Ozolins, A. Udalcovs, R. Schatz,

S. Popov, G Jacobsen, “Design of Multi-Stage Carrier Phase Recovery Schemes

for high order Coherent Optical mQAM Systems,” J. Lightwave Technol.,

submitted.

Paper VIII: A. Kakkar, J. Rodrigo Navarro, R. Schatz, H. Louchet, X. Pang, O. Ozolins, G.

Jacobsen, S. Popov, "Comprehensive Study of Equalization-Enhanced Phase

Noise in Coherent Optical Systems," IEEE/OSA J. Lightwave Technol. 33(23),

4834-4841 (2015).

Paper IX: A. Kakkar, R. Schatz, X. Pang, J. Rodrigo Navarro, H. Louchet, O. Ozolins, G.

Jacobsen, S. Popov, "Impact of local oscillator frequency noise on coherent

optical systems with electronic dispersion compensation," Opt. Express 23(9),

11221-11226 (2015).

Paper X: A. Kakkar, X. Pang, O. Ozolins, R. Schatz, J. Rodrigo Navarro, H. Louchet, G.

Jacobsen, S. Popov, “A Path to Use Large Linewidth LO in 28 Gbd 16-QAM

Metro Links”, in Proc. of ECOC 2015 (OSA/IEEE, 2015), paper Tu.3.4.6.

Paper XI: A. Kakkar, J. Rodrigo Navarro, R. Schatz, X. Pang, O. Ozolins, H. Louchet, G.

Jacobsen, S. Popov, "Mitigation of EEPN in Coherent Optical Systems With

Low-Speed Digital Coherence Enhancement," IEEE PTL, 27(18), 1942-1945

(2015).

http://dx.doi.org/10.1109/lpt.2015.2455234http://dx.doi.org/10.1109/lpt.2015.2455234http://dx.doi.org/10.1109/jlt.2016.2545339http://dx.doi.org/10.1109/jlt.2016.2545339http://dx.doi.org/10.3390/photonics3020037http://dx.doi.org/10.3390/photonics3020037http://dx.doi.org/10.3390/photonics3020037http://dx.doi.org/10.1109/ecoc.2015.7341657http://dx.doi.org/10.1109/ecoc.2015.7341657http://dx.doi.org/10.1109/jlt.2015.2491363http://dx.doi.org/10.1109/jlt.2015.2491363http://dx.doi.org/10.1364/oe.23.011221http://dx.doi.org/10.1364/oe.23.011221http://dx.doi.org/10.1109/ECOC.2015.7341948http://dx.doi.org/10.1109/ECOC.2015.7341948http://dx.doi.org/10.1109/lpt.2015.2447839http://dx.doi.org/10.1109/lpt.2015.2447839

xvi LIST OF PUBLICATIONS

Paper XII: A. Kakkar, M. Iglesias Olmedo, O. Ozolins, J. Rodrigo Navarro, X. Pang, R.

Schatz, H. Louchet, G. Jacobsen, S. Popov, “Overcoming EEPN in Coherent

Transmission Systems”, in Proc. of CLEO 2016 (OSA, 2016), paper SM4F.3.

Paper XIII: A. Kakkar, J. Rodrigo Navarro, R. Schatz, X. Pang, O. Ozolins, H. Louchet, G.

Jacobsen, S. Popov, “Equalization Enhanced Phase Noise in Coherent Optical

Systems with Digital Pre- and Post-Processing,” Photonics 3(2), 12 (2016).

Paper XIV: A. Kakkar, O. Ozolins, J. Rodrigo Navarro, X. Pang, M. I. Olmedo, R. Schatz,

H. Louchet, G. Jacobsen, S. Popov, “Design of Coherent Optical Systems

Impaired by EEPN”, in Proc. of OFC 2016 (OSA, 2016), paper Tu2A.2.

Paper XV: A. Kakkar, J. Rodrigo Navarro, R. Schatz, X. Pang, O. Ozolins, A. Udalcovs,

H. Louchet, S. Popov, G. Jacobsen, “Laser Frequency Noise in Coherent Optical

Systems: Spectral Regimes and Impairments,” Scientific Reports, vol. 7, Art. no.

844 (2017).

Paper XVI: A. Kakkar, J. Rodrigo Navarro, R. Schatz, X. Pang, O. Ozolins, F. Nordwall,

D. Zibar, G. Jacobsen, S. Popov, “Influence of Lasers with Non-White Frequency

Noise on the Design of Coherent Optical Links,” in OFC 2017, (OSA, 2017),

paper Th2A.55.

Publications not included in this thesis:

Paper I: A. Kakkar, J. Rodrigo Navarro, X. Pang, O. Ozolins, R. Schatz, U. Westergren,

G. Jacobsen, S. Popov, “Low Complexity Timing Recovery Algorithm for PAM-

8 in High Speed Direct Detection Short Range Links,” in Proc. Of OFC2017

(OSA, 2017), paper W2A.54.

Paper II: S. Popov, A. Kakkar, J. Rodrigo Navarro, X. Pang, O. Ozolins, R. Schatz,

H. Louchet, G. Jacobsen, “Equalization-Enhanced Phase Noise in Coherent

Optical Communications Systems”, in Proc. of ICTON 2016.

Paper III: J. Rodrigo Navarro, A. Kakkar, X. Pang, O. Ozolins, A. Udalcovs, R. Schatz,

and G. Jacobsen, S. Popov, “64-QAM Coherent Optical Systems with

Semiconductor Lasers,” Invited talk at PIERS2017, St Petersburg, Russia, 22nd

– 25th of May, 2017

Paper IV: X. Pang, J. Rodrigo Navarro, A. Kakkar, M. Iglesias Olmedo, O. Ozolins, R.

Schatz, A. Udalcovs, S. Popov, G. Jacobsen, “Advanced Modulations and DSP

enabling High-speed Coherent Communication using Large Linewidth Lasers,”

in Proc. of PIERS 2016, p. 1-1.

Paper V: O. Ozolins, M. Iglesias Olmedo, X. Pang, S. Gaiarin, A. Kakkar,

J. Rodrigo Navarro, A. Udalcovs, K. M. Engenhardt, T. Asyngier, R. Schatz, J.

Li, F. Nordwall, U. Westergren, D. Zibar, S. Popov, G. Jacobsen, “100 GHz EML

for High Speed Optical Interconnect Applications,” IEEE/OSA J. Lightwave

Technol., Invited paper accepted.

Paper VI: X. Pang, O. Ozolins, S. Gaiarin, A. Kakkar, J. Rodrigo Navarro, M. Iglesias

Olmedo, R. Schatz, A. Udalcovs, U. Westergren, D. Zibar, S. Popov G. Jacobsen,

“Experimental Study of 1.55-µm EML-Based Optical IM/DD PAM-4/8 Short

Reach Systems,” IEEE Photonics Technology Letters, accepted

http://dx.doi.org/10.1364/cleo_si.2016.sm4f.3http://dx.doi.org/10.1364/cleo_si.2016.sm4f.3http://dx.doi.org/10.3390/photonics3020012http://dx.doi.org/10.3390/photonics3020012http://dx.doi.org/10.1364/ofc.2016.tu2a.2http://dx.doi.org/10.1364/ofc.2016.tu2a.2

LIST OF PUBLICATIONS xvii

Paper VII: O. Ozolins, X. Pang, M. Iglesias Olmedo, A. Udalcovs, A. Kakkar, J. Rodrigo

Navarro, R. Schatz, U. Westergren, S. Popov, G. Jacobsen, “High-Speed Optical

and Wireless Transmission – Challenges and Achievements” in Proc. of

RTUWO2016 (IEEE, 2016), p. 1.

Paper VIII: S. Popov, X. Pang, O. Ozolins, M. Iglesias Olmedo, A. Kakkar, S. Gaiarin, A.

Udalcovs, R. Lin, R. Schatz, J. Rodrigo Navarro, A. Djupsjöbacka, D. Zibar, J.

Chen, U. Westergren, G. Jacobsen, ” Ultra-Broadband High-Linear Integrated

Transmitter for Low Complexity Optical Interconnect Applications” in Proc. of

ACP2016 (OSA, 2016), p. 1.

Paper IX: O. Ozolins, X. Pang, M. Iglesias Olmedo, A. Kakkar, A. Udalcovs, J. Rodrigo

Navarro, R. Schatz, U. Westergren, G. Jacobsen, S. Popov, “High-speed Optical

Interconnects with Integrated Externally Modulated Laser,” Invited talk at

ICTON 2017, Girona, Spain, 2nd - 6th of July 2017.

Paper X: A. Marinins, O. Ozolins, X. Pang, A. Udalcovs, J. Rodrigo Navarro, A. Kakkar,

R. Schatz, G. Jacobsen, S. Popov, “Cylindrical Polymer Optical Waveguides with

Polarization Independent Performance,” in CLEO2017 (OSA, 2017), submitted.

1

Chapter 1

Introduction

The parallel invention of semiconductor laser diodes together with photo-detectors and the

realization of the first low-loss fiber in 1970 by Corning Glass may be considered as the origin of

a new field, optical telecommunications [1-3]. This new technology had the potential to offer

virtually “infinite” bandwidth compared to earlier coaxial and free-space radio based transmission

systems. In this chapter, we provide an overview of the historical developments of optical

communications from its initial days to the present modern coherent optical communication

systems.

1.1 Historical Background

It was not until 2005 where coherent optical communications regain widespread interest. Up until

then, traditional intensity-modulation direct-detection (IMDD) schemes employed in wavelength-

division multiplexed (WDM) systems along with the development of the erbium-doped amplifier

(EDFA) were the main research focus [1]. We treat the historical developments of traditional

systems and modern coherent communication systems separately in this chapter.

1.1.1 History of Traditional Direct-Detection Optical Communications

The vision that fiber waveguide could be used to transmit laser-light signals corresponds to

C. A. Hockham and C. K. Kao who, later in 2009, was awarded the Nobel Prize for the invention

of fiber optics [3]. In order to trap the light inside the fiber core, a cladding surrounding the core

with slightly lower refractive index was added to produce total internal light reflection. Analytical

studies on graded refractive-index optical waveguides with power-law profiles were proposed in

the late 1960s before the introduction of low-loss fibers [5,6]. However, the challenge remained

finding an appropriate material for making fiber glass. In the 1960s, the attenuation of the best

silica glass was of 1dB per meter at 0.8μm of wavelength which was impractical for transmission.

The elimination of glass impurities led to the historical development of a single mode fiber with

2 CHAPTER 1. INTRODUCTION

20 dB/km of losses [4,7]. Subsequent efforts were made to reduce OH impurity resulting in fiber

losses of 0.2 dB/km at 1.55μm of wavelength [7]. Nowadays, optical fibers have attenuations of ≈

0.16 dB/km over the 1.55μm transmission band.

Along with the development of low-loss fibers, light sources such as lasers and LED’s were the

focus of intensive research for practical implementation of fiber transmission systems [7]. The first

semiconductor laser, made of GaAs, was reported in 1962 followed with the development of

AlGaAs lasers within the next 8 years [8]. These early devices had a short lifetime ranging from

few minutes to few hours and therefore impractical for stable long-term optical communication

systems. Since then, compact and efficient semiconductor laser chips emitting at 1.3 μm and 1.55

μm have been developed with sufficient high efficiency and reliability to compose the basics of

optical communications technology [8].

Fiber losses, however, were still the main problem to transmit information over long distances.

The optical signal had to be electrically regenerated meaning that the optical signals had to be

converted into electrical signals, electronically amplified, converted back into optical and launched

into the fiber in the following fiber span. The invention of the optical fiber amplifier was the key

milestone to overcome this problem. The erbium doped fiber amplifier (EDFA) and its

manufacturing challenges were investigated around 1987-1988 in the university of Southampton

and Bell Laboratories [9-11]. The properties of the EDFA had the potential to simultaneously re-

amplify different several signals at different wavelengths without interference between them which

gave rise to the wavelength-division multiplexing (WDM) scheme. However, with the demand for

more throughput significantly increasing, the sole utilization of WDM and EDFA rapidly became

insufficient as problems with nonlinearities and chromatic dispersion started to appear in these

schemes. The two existing type of optical fibers in the 1990s could not cope with large-channel-

count WDM at bit rates above 2.5Gb/s [12]. The existing standard single-mode fiber (SSMF) had

a large chromatic dispersion in the 1550 nm band which limited the transmission reach of 10 Gb/s

signals to only 60km. The dispersion-shifted fiber (DSF) was developed precisely to reduce the

chromatic dispersion problems in the 1550nm band. However, this type of fiber turned out to be

more vulnerable to the optical nonlinear effect four-wave mixing (FWM). A new non-zero

dispersion shifted fiber was developed at Bell Labs in 1993 with low enough dispersion to transmit

10Gb/s over hundreds of kilometers but with sufficient dispersion to destroy the phase matching

condition necessary for the FWM phenomena to appear. With 40 Gb/s in the horizon, dispersion

CHAPTER 1. INTRODUCTION 3

management and dispersion compensating (DCF) fibers were developed in what we can identify

as the dispersion managed WDM era (1993-2009). During this era, relevant improvements such

as forward error correction (FEC), Raman amplification and polarization multiplexing where also

introduced. By the end of this era commercial systems were available with up to 80 wavelengths

operating each at 40 Gb/s. Eventually, EDFAs ran out of optical bandwidth and “packing” more

data into a given slice of spectrum could only be achieved by employing higher efficient

modulations. The early studies about coherent detection developed in the 1980s were then revived

as the next promising technology to further increase the transmission capacity.

1.1.2 Coherent Optical Communications

It was only after 2000 where coherent technologies attracted a renewal of widespread interest due

to the increase in capacity demand which traditional EDFA+WDM schemes could not cope with.

Higher receiver sensitivity and the possibility to use high spectral efficient modulations are two of

the main advantages of coherent detection. Multilevel modulation formats based on coherent

technologies rapidly became the mainstream research with the quadrature phase shift keying

(QPSK) modulation scheme as the first step [13]. Recent developments of high-speed digital

integrated circuits triggered the possibility of retrieving the “In phase” (I) and “Quadrature” (Q)

signal components from the complex amplitude of an optical carrier by means of processing the

high-speed electrical signals in a DSP core. The demodulation of a 20 Gb/s QPSK using homodyne

detection followed by digital carrier phase estimation in DSP was reported in [14]. Although carrier

phase recovery (CPR) could be achieved with an optical phase locked loop, its intrinsic feedback

delay problem caused the phase recovery to be preferably performed in DSP after homodyne

detection. This type of receiver was then called “digital coherent receiver” having the ability to

employ any type of multi-level modulation format as both the amplitude and the phase of an optical

carrier could be recovered in a stable manner. Owing to the linearity of the IQ demodulation

process, all the information of the transmitted optical signal is preserved after detection and DSP

for transmission impairment mitigation can be performed on the detected electrical signals.

Polarization alignment could also be achieved by its corresponding DSP routine in a polarization-

diversity homodyne receiver.

The achievement of an ASIC-based real-time 46 Gb/s transmission in 2008 is considered a

milestone for modern coherent optical communications [4,15]. The combination of ASIC and DSP

is nowadays leading the path of coherent optical communications enabling features not possible in


traditional non-coherent systems. Current commercial systems have demonstrated 127 Gb/s

transmission with a 27% overhead for FEC accounting for a total capacity of 8 Tb/s in a WDM

system with a 50 GHz grid interval [16]. These achievements confirm coherent detection together

with DSP as key enablers for the PETA transmission era.

1.2 Phase Noise in Coherent Optical Systems

In order to increase the data rate further, high spectral efficient modulation formats such as 16QAM

or beyond are under extensive research. However, high spectral efficient modulations are more

susceptible to the different impairments and distortions occurring during signal generation,

transmission and reception as its constellation points are more “packed” in the complex plane. The

impairments arising in these systems can be mainly classified into AWGN, fiber non-linearities,

chromatic dispersion, polarization mode dispersion and phase noise related issues. The non-

spectral purity of the lasers employed for signal modulation/demodulation in coherent optical

systems generally translates into phase noise impairment in the detected signal. Thus, considering

that in these modulation formats the data is encoded in the amplitude and phase of an optical carrier,

the mitigation of the phase noise becomes a critical step to properly recover the transmitted data.

Nowadays, research mainly focuses in performing CPR in the electrical domain as part of the DSP

core [17]. CPR schemes can generally be classified into feedforward and feedback architectures.

Feedback CPR structures employs the phase noise estimator of previous symbols to compensate

for the phase noise of current symbols. In feedforward structures, a phase noise estimator is

computed from a block of symbols and is used to compensate for the phase noise of the symbols

within the same block. Owing to the high parallelization and pipelining required in a real ASIC

implementation of the DSP, the feedback delay required in feedback structures limits ultimately

its performance and feedforward architectures are often preferred [18-21]. The Viterbi and Viterbi

(V&V) feedforward algorithm employs the non-linear M-th power operation to remove the

modulation component of M-ary PSK modulated symbols as their angular modulation is uniformly

distributed in the complex plane [22]. However, its scalability to more general m-QAM modulation

formats is not straight forward as, in these cases, the angular modulation component of all

constellation points cannot by directly removed by the M-th power operation. Different schemes

have been proposed to adapt the V&V CPR to 16QAM and 64QAM which are generally based on

the QPSK partitioning approach [23-25]. However, this approach results in a limited phase noise

tolerance as only a small percentage of the constellation points can be used for phase noise

CHAPTER 1. INTRODUCTION 5

estimation in high order modulation formats. Recently, the blind phase search (BPS) CPR scheme

has become popular due to its good phase noise tolerance and scalability to high order modulations

[18]. In this approach, the received signal is de-rotated by a number of “test phases”. The test phase

which de-rotates the received signal the closest to the ideal constellation is considered to be the

phase noise estimator. Although this approach has good phase noise tolerance, it comes with the

drawback of a high computational complexity as the required number of test phases drastically

increases with the modulation order. Alternatively, the task of CPR can be performed by inserting

pilot symbols in the received sequence at the cost of reducing the net symbol rate [26,27].

Altogether, CPR is under extensive research and high phase noise tolerant CPR schemes scalable

to high order modulations at low implementation complexity levels are yet to be defined. This task

becomes even more important as the industry transitions towards pluggable coherent transceivers

where power consumption and integration becomes critical.

The possibility to extract the phase information of the received data during coherent detection

enables the compensation of chromatic dispersion in the electrical domain as a part of the DSP

routine. However, under certain conditions of accumulated dispersion and local oscillator phase

noise, it has been reported that the electronic compensation of the dispersion results in an enhanced

noise in both the amplitude and phase domains known as equalization enhanced phase noise [28-

31]. The general consensus for the explanation of this phenomenon lies in the fact that, in these

systems, the phase noise from the LO laser passes directly through the chromatic equalization

module where it gets dispersed. Hence, creating a complex interaction between the received signal

and the dispersed LO laser. Despite the given explanation and all research efforts to characterize

this added noise, many questions still remained unanswered. Furthermore, all studies were

performed based on a statistical view of the phenomenon considering lasers with a white frequency

noise spectrum. However, a thorough analytical investigation of the phenomena employing a more

realistic non-white laser frequency noise spectrum is required.

1.3 Overview of the Thesis Contribution

In this thesis, we contribute in addressing the problems listed in the previous section which can be

divided into:

• High phase noise tolerant and low implementation complexity CPR schemes for high order

modulations.


• Analytical study of the equalization enhanced phase noise (EEPN) phenomenon for general

non-white laser frequency noise spectrums.

Phase noise compensation for high spectral efficient modulations at low implementation

complexity levels becomes a difficult task due to the lack of suitable CPR schemes for this type of

modulation formats. The first approach provided in this thesis explores the possibility of re-

arranging the constellation points of a conventional square mQAM modulation format in a

circularly shaped mQAM constellation. This constellation inherently provides higher phase noise

tolerance and traditional low-complex algorithms based on the V&V scheme can be directly

applied. The advantages, drawbacks and the performance of different novel proposed CPR

schemes for this kind of modulations are investigated and compared to that of conventional square

mQAM systems. Secondly, we make a thorough investigation of the state-of-the-art BPS algorithm

to reveal the inherent angular quantization noise limitation of the algorithm due to its angle

discretization nature. We demonstrate that, by applying a low pass filtering operation in the BPS

phase noise estimator for quantization noise mitigation, its performance can be improved and its

implementation complexity can be drastically reduced. The outcomes of this work in terms of

performance increase and complexity reduction are considered as an addition to existing research

efforts as we tackle a different unreported problem. All outcomes of this research are validated

experimentally in a 28Gbaud coherent optical transmission system employing up to 64QAM

constellations.

We revise the origin of the EEPN phenomena by performing a thorough analytical study which

reveals that EEPN is mainly caused due to a frequency noise induced symbol jitter. Particularly,

we show that the laser frequency noise spectrum can be divided into different regimes each of

them causing a different set of impairments in the system. In order to possibly mitigate these

impairments, we show that different DSP optimization techniques apply for different spectral

regimes. The proposed EEPN theory is supported by system simulations and validated

experimentally in 28Gbaud coherent optical transmission systems employing up to 64QAM

constellations.

7

Chapter 2

Coherent Optical Fiber Communication

Systems

The possibility to encode data in the amplitude and phase domains of an optical carrier wave allows

the use of spectrally efficient modulation formats in coherent optical communication systems. In

contrast to traditional IMDD systems, the received signal in coherent communication systems is

mixed with a local oscillator in order to extract the phase information of the received optical carrier.

In this chapter we briefly describe the main modules that model a coherent optical fiber-based

communication system: transmitter, channel and DSP based receiver.

2.1 Transmitter

The transmitter modulates the incoming bit stream into the phase and amplitude of an optical

carrier wave according to a given modulation format. Figure 2.1 shows the general schematic of a

DSP-based optical transmitter employing polarization diversity [32]. The incoming bit stream is

passed to the DSP module where different routines can be applied such as signal pre-distortion/pre-

compensation, Nyquist pulse shaping etc. After the DSP module, the DACs recreate the analog

signals which drive a pair of Mach Zehnder modulators (MZM) according to a given modulation

format. The MZMs modulate the “In phase” and “Quadrature” components of both polarizations

of the transmitting laser carrier wave in a polarization diversity based transmitter. Both

polarizations are then combined in a polarization beam combiner (PBC) resulting in the output

optical signal of the transmitter.

2.1.1 Modulation Formats

In order to transmit the input binary sequence, the optical transmitter encodes the incoming bits

into one or multiple dimensions of the transmitting laser optical carrier wave. High efficient

modulation formats encode information in both the amplitude and phase domains of the carrier

8 CHAPTER 2. COHERENT OPTICAL FIBER COMMUNICATION SYSTEMS

Figure 2.1: General structure of a DSP-based optical transmitter

wave. In order to achieve this, the optical transmitter in Figure 2.1 separately modulates the

orthogonal In phase and Quadrature components of the transmitter laser carrier wave. The In

phase and Quadrature components are created by splitting the optical carrier wave and applying a

π/2 phase shift to one of the branches. Then, the amplitude of both components is separately

modulated to generate complex symbols. In order to illustrate the process let the amplitude and

phase modulated of an optical carrier wave be,

cosopt k k

x t A wt p t kD (2.1)

Where Ak and k represent the amplitude and phase modulation of the k-th symbol respectively

while D and w represent the symbol period and central carrier frequency respectively and p(t)

represents the unity pulse function. Eq. 2.1 can be rewritten in the following form

cos cos cos2

opt k k k kx t A wt p t kD I wt Q wt p t kD

(2.2)

Where I and Q represent the In phase and Quadrature components of the optical carrier wave as

cosk k k

I A (2.3)

sink k k

Q A (2.4)

Since the In phase and Quadrature components are orthogonal to each other it is therefore

convenient to represent them in a two dimensional plane known as the complex plane. All the

possible I and Q combinations in the complex plane for a given modulation format is known as

DSP

DA

CD

AC

Tx Laser

PBS PBC

”X” pol.

”Y” pol.

1 0 1 0

2

2

CHAPTER 2. COHERENT OPTICAL FIBER COMMUNICATION SYSTEMS 9

Figure 2.2: Square 16QAM and circular 16QAM constellations in the complex plane

constellation. It is noted that by separately modulating the I and Q components of the optical carrier

wave it is possible to locate any symbol at any point in the complex plane, thus allowing the

possibility to create any constellation shape. Figure 2.2 illustrates the shape of a square 16QAM

and a circular 16QAM constellation.

2.1.2 Pulse Shaping Filter

The use of pulse shaping filters in communications is justified when employing band limited

channels. The main purpose of the pulse shaping filter is to generate band limited signals in order

to accommodate the signals to the channel frequency response and to avoid inter symbol

interference [33,34]. Therefore, it is important to consider the utilization of pulse shaping in the

DSP block of the optical transmitter in Figure 2.1. Generally, the frequency response of a Nyquist

pulse shaping filter can be written as

10

2

1 11 cos 2 1

2 2 2 2

0

T fT

TH f fT f

T T

otherwise

(2.5)

Where T and are the symbol period and the roll-off factor respectively.

In Phase In Phase

Quadrature Quadrature

16 QAM C-16QAM


Figure 2.3:. Dual-nested Mach-Zender modulator structure

2.1.3 Dual-nested IQ Mach-Zehnder modulator (IQ MZM)

Figure 2.3 illustrates the structure of a dual-nested IQ Mach-Zehnder modulator (IQ MZM) as a

part of the optical transmitter shown in Figure 2.1 [4]. The transfer function of the nested IQ MZMs

when biased at minimum transmission points and operating in push pull modes can be defined as

(t)(t) 1 (t) 1

cos cos(t) 2 2 2 2

Qout I

in

Ej

E

(2.6)

,I QI Q

u t u tt t

V V

(2.7)

Where V is the voltage required to produce a phase shift of π and Iu t and Qu t are the driving

signals applied to the In phase and Quadrature branches respectively. Therefore, by applying

different driving signals to the In phase and Quadrature branches we can independently change

their amplitudes and create different complex symbols at the output. The MZM must be operating

near the linear region of its transfer function to avoid symbol distortions. If polarization diversity

is employed, this structure is replicated for each of the polarizations as illustrated in the

polarization diversity transmitter of Figure 2.1.

2.1.4 Laser sources

In coherent optical communications the data is encoded in the amplitude and phase of an optical

carrier wave. In these systems, lasers are used as optical sources due to its narrower optical

spectrum as compared to other optical sources such as LEDs. The normalized output of the

transmitting laser can be modeled as

Ein (t) Eout (t)

uI (t)

uQ (t)2

V


( (t) (t))tx pnj wLaser

x t e

(2.8)

Where Tx

w and pn

represent the central emitting frequency and the phase noise of the laser

respectively. Generally, phase noise can be modeled as a Wiener process [18]

1pn pn pn

k k k (2.9)

Where pn

k is an independent and identically distributed random Gaussian variable with zero

mean and variance [18]

2 2pn s

f T

(2.10)

In this formula f corresponds to the linewidth of the signal laser and s

T corresponds to the

symbol period. In this case, the linewidth shape corresponds to a Lorentzian function. The before

mentioned assumptions correspond to a laser with a white frequency noise spectrum generally

considered for modeling coherent optical systems [35,36]. However, a more realistic case

corresponds to a non-white frequency noise spectrum which can be written as [37]

1

9 4

2int

22 2

2 2

101

1

2

f R

R

R

fS f

f kff f

(2.11)

Where 1

f

describes the level of 1/f noise at 1 GHz; int corresponds to the level of intrinsic

frequency noise at low frequencies; R

f is the resonance frequency and the K-factor describes how

the damping rate increases with relaxation frequency. The parameter determines the carrier

induced frequency noise that gives rise to the noise peak around the resonance frequency.

2.2 Optical Fiber Channel

Attenuation, dispersion, polarization mode dispersion and fiber nonlinearities are the main

impairments impacting the signal during its transmission through the fiber in optical fiber

communication systems. In this section we give a brief description about these impairments for

single mode fibers.


2.2.1 Attenuation in Optical Fibers

The concept of attenuation in optical fibers relates to the power loss of an optical signal as it travels

through the fiber. In unrepeated optical communication systems, attenuation limits the achievable

transmission distance as the receiver requires a minimum input signal power to produce a given

signal to noise ratio in its output specified by the receiver sensitivity. The relation between the

average power of the propagating signal “P” and the distance traveled “z” can be expressed as

P

Pz

(2.12)

Where defines the attenuation coefficient. By solving the differential eq. 2.12 we obtain

L

out inP P e (2.13)

Where out

P and in

P represent the output and input signal powers respectively after signal

propagation trough a distance L . Attenuation is often expressed in dB/km

10

10log 4.343out

in

dB P

km L P

(2.14)

The mechanisms leading to fiber attenuation can be classified into extrinsic and intrinsic

mechanisms. The intrinsic mechanisms are related to the material chosen to manufacture the

optical fiber and are unavoidable. The extrinsic mechanisms are due to external factors of the

optical fiber material and could be avoidable. Ultraviolet attenuation, infrared attenuation and

scattering Rayleigh are amongst the intrinsic mechanisms while fiber-impurities such as hydrogen,

OH ions and metallic impurities or fiber curvatures pertain to the extrinsic mechanisms. Ultraviolet

attenuation is caused due to electronic transitions between the valence and conduction bands of

the material that composes the fiber generating a resonance frequency outside the transmission

band but whose tails extend to the transmission band. Infrared attenuation is due to the existence

of intense absorption bands originated by vibrations and oscillations of the structure that compose

the fiber material at those frequencies. Scattering Rayleigh is due to local fluctuations, smaller

than the operating wavelength, of the dielectric constant (refractive index) of the material that

composes the fiber. The presence of impurities in the fiber causes intense absorption bands which

can be mitigated by controlling the amount of impurities in the fiber. Optical fiber curvatures,

forces part of the light to travel a longer distance (external part of the curvature) in the same time


in order to maintain the transmitting mode. This is impossible as the light velocity is constant

resulting consequently in light radiation outside the fiber.

2.2.2 Fiber Dispersion

Chromatic dispersion is one of the main impairments affecting the signal as it travels through the

fiber in optical communication systems employing single mode fibers. The different spectral

components that compose the transmitted signal travel at different speed through the fiber causing

signal distortion [38]. In digital optical fiber communications where the information is transmitted

by means of light pulses, chromatic dispersion results in pulse broadening causing inter symbol

interference. In order to mitigate the impact of chromatic dispersion, the signal bandwidth and/or

the transmission reach has to be reduced. Thus, chromatic dispersion limits the transmission reach

and/or the transmission capacity.

There exist two main dispersion mechanisms which can be separately analyzed: Material

dispersion and waveguide dispersion. Material dispersion is caused due to a frequency dependence

of the dielectric constant of the materials that compose the optical fiber. This means that the

materials that compose the core and cladding of a fiber are dispersive materials. It is noted that

material dispersion is independent from whether these materials form a waveguide or not.

Waveguide dispersion is caused due to a frequency dependence of the propagation constant in a

waveguide. By employing the Taylor series expansion of the propagation constant (β(w)) around

the working point w0 we obtain [38]

0 0 0

2 32 3

0 0 0 02 3

1 1...

2 6w w w

w w w w w w w ww w w

(2.15)

Therefore, we can define the group delay per unit length as

2

1 2 0 3 0

10 ...

2

gw

w w w wL w

(2.16)


Figure 2.4: Group delay per unit length considering β2 a) and β3 b) dispersion terms.

We can observe from eq. 2.16 that the β1 term causes a constant group delay for all frequencies

while the β2 and β3 terms correspond to a linear and quadratic variation of the group delay

respectively with respect to w. Figure 2.4 shows the group delay for the cases where β2 ≠ 0 >> β3

and β2 = 0 .

The dispersion parameters for both cases “D” and “S” can be defined as

2

2 32 2

2 2,

c cD S

(2.17)

Eq. 2.17 allows us to work with instead of w

21

,8

T L D T L S (2.18)

2.2.3 Polarization Mode Dispersion

Polarization mode dispersion is caused due to fiber birefringence. Optical fibers are not perfectly

cylindrical due to tensions and torsions. Moreover, the relative position between core and cladding

might not be constant along the fiber. Therefore, two orthogonal polarizations travel at different

speeds in the fiber as they perceive different refractive indexes due to fiber birefringence. Fiber

birefringence is not constant through the fiber and it randomly changes due to temperature

variations which randomly changes the state of the polarization in the fiber. Polarization mode

dispersion can be defined as

T PMD L (2.19)

Where PMD and L are the polarization mode dispersion parameter and fiber length respectively.

g w

L

w0w

w

2

Tw

L

1

g w

L

w0w

w

2

3

1

8

Tw

L

2

1 3 0

1

2

g ww w

L

1 2 0

g ww w

L

a) b)


Figure 2.5: Coherent optical receiver structure with polarization diversity.

2.3 Coherent Optical Receiver

A digital coherent optical receiver employing polarization diversity is shown in Figure 2.5. The

coherent optical receiver structure shown in Figure 2.5 is composed of an optical front-end, analog-

to-digital converters and a digital signal processing block. A linearly polarized local oscillator

centered at w0 is used to demodulate the received optical signal. The local oscillator output and the

received signal are firstly split into two “x” and “y” orthogonal polarizations and fed into the

ninety degree hybrids having a transfer function as shown in Figure 2.6 [4]. The outputs of the

ninety degree hybrid fall then into the square-law photodetectors for signal demodulation and the

In phase and Quadrature signal components for each of the polarizations can be recovered [4].

The recovered In phase and Quadrature signal components are then sampled and passed to the

DSP module for further signal processing.

Figure 2.6: Ninety degree hybrid transfer function.

PBS

90o Hybrid X-Pol

90o Hybrid Y-PolLO

LaserPBS

AD

CA

DC

AD

CA

DC

DSP

Pro

cess

ing

Ix

Qx

Iy

Qy

1

2 1

3 2

4

1 1

1 11

12

1

O

O I

O Ij

O j

I1

I2

Es

ELO

O1

O2

O3

O4


2.3.1 Analog-to-Digital Converters

The analog-to-digital converters sample the In phase and Quadrature signal components of both

polarizations in a polarization diversity coherent optical receiver. The sampling rate of the ADCs

needs to be high enough in order to preserve all the spectral information for a further post-sampling

DSP according to sampling theory [39]. The received In phase and Quadrature signals must be

sampled at a rate of at least twice the bandwidth of these signals according to the Nyquist theorem

to avoid aliasing. Due to the high data rates used in fiber-optic systems and the difficulty of

manufacturing high-speed sampling ADCs, the ADCs might limit the transmission speed in these

systems [17]. Two important characteristics of an ADC are its bit resolution and its full scale

voltage range (FSR). Quantization noise is added in the sampled signals by the ADCs due to the

limited bit resolution of the ADCs. The FSR parameter refers to the maximum voltage range in

which the signal to be sampled should be contained for a proper sampling. If the signal to be

sampled exceeds the limits given by the FSR parameter it will result in signal clipping. This

problem can be alleviated by using a signal automatic gain control (AGC) in order to maintain the

signal within the limits specified by the FSR parameter.

2.4 Digital Signal Processing

Once the In phase and Quadrature signals are sampled according to the Nyquist theorem, digital

signal processing can be used to mitigate the impairments that have occurred during signal

generation, reception and/or transmission. In this section, we give a brief description of the basic

DSP modules that compose a coherent optical receiver as illustrated in Figure 2.7.

Figure 2.7: DSP modules that compose the DSP processing block in a coherent optical receiver.

Sta

tic

Ch

an

nel

Eq

ua

liza

tio

n

De-

Skew

an

d O

rth

on

orm

aliz

ati

on

Dyn

am

ic C

ha

nn

el E

qu

aliz

ati

on

Freq

uen

cy O

ffse

t C

om

pen

sati

on

Ca

rrie

r P

ha

se E

stim

ati

on

Sym

bo

l Est

ima

tio

n a

nd

Dec

od

ing

Digital Signal Processing Modules

Inte

rpo

lati

on

an

d T

imin

g R

eco

very


2.4.1 De-Skew and Orthonormalization

The purpose of the de-skew subsystem is to compensate for path length mismatches between the I

and Q channels in the optical front end and for each of the polarizations [17,40]. Therefore, the de-

skew subsystem synchronizes both I and Q signals in time. As the time mismatch between the

channels might be less than the sampling rate of the ADCs, an interpolator is needed in order to be

able to compensate for time delays lesser than the sampling rate of the ADCs [17,40]. The

orthonormalization algorithm compensates for possible imperfections in the ninety degree hybrids

[17]. The ninety degree phase shift needed in one of the branches of the hybrid might not be

perfectly achieved leading to an orthogonalization problem between its output ports. Two

algorithms are normally employed to compensate for orthogonalization problems in the ninety

degree hybrid based on the Gram-Schmidt and the Löwdin orthogonalization processes. The

Gram-Schimdt takes one received vector as a reference against which all subsequent created

vectors are orthogonalized [41-43]. The Löwdin algorithm creates a set of vectors orthogonal to

each other which are closer to the original vectors in a least-mean squares sense [44,45].

2.4.2 Static Channel Equalization

The recovery of the optical field in coherent detection allows compensating for transmission

impairments such as chromatic dispersion or polarization mode dispersion. The compensation of

chromatic dispersion and time-varying effects such as PMD is conventionally done separately in

the static and dynamic channel equalization modules respectively. This is mainly due to the use of

large static and short adaptive filters for each of the phenomena respectively [17,46,47]. The effect

of chromatic dispersion on the transmitted signal can be compensated by applying the inverse

frequency channel response

1( ) j z

cH w e (2.20)

Chromatic dispersion compensation can be performed either in time or frequency domains.

However, it is preferably performed using efficient FIR implementations in frequency domain with,

for instance, the overlap-add method [17,48].

2.4.3 Interpolation and Timing Recovery

After signal static equalization for channel chromatic dispersion compensation, it is possible to

compensate for the differences between the transmitter clock and the sampling rate of the ADCs


in the coherent receiver. The task of the timing recovery module is to synchronize the receiver

clock with that used in the transmitter in order to produce samples of the received signal with

optimal SNR [17]. Timing recovery can be performed prior to the subsequent DSP algorithms as

shown in Fig 2.7. Some of the implementations of subsequent algorithms use the properties of the

constellation for impairment mitigation assuming therefore, clock synchronization. Commonly,

timing recovery is performed by means of interpolation and timing phase estimation in non-data

aided timing recovery algorithms [49,50]. Assuming the received signal to be sampled at the

Nyquist rate or higher, the task of the interpolator is to generate approximated samples of the

received signal in between the ADCs samples. This can be achieved by means of interpolation by

adding zeros in between the ADC samples followed by a low pas filter. Then, the timing phase

estimator uses these samples to test a cost function in order to decide the optimal sampling point.

Different algorithms employing a diversity of cost functions have been proposed such as Gardner,

Godard, Lee or the CMA algorithms [50-53].

2.4.4 Dynamic Channel Equalization

In this module, time varying impairments such as state of polarization or PMD are compensated

[17]. Fig 2.8 shows an adaptive equalizer structure which may be employed for the correction of

these dynamic effects. The MIMO structure shown in Fig. 2.8 aims to perform the inverse Jones

matrix of the dynamic channel resulting in the pair of outputs [17,54],

H H

out xx in xy in

H H

out yx in yy in

x k h k x k h k y k

y k h k x k h k y k

(2.21)

In contrast to the static channel equalizer, the number of taps required for this equalizer is typically

less. In order to achieve polarization demultiplexing at the receiver, the constant modulus

algorithm (CMA) can be employed [17,55]. The CMA algorithm makes use of the constant symbol

amplitude property in single amplitude level constellations such as QPSK or BPSK to evaluate a

cost function. The taps of the filters are updated following a gradient descendant approach of the

given cost function. For constellations having different amplitude levels, a multimodulus based

algorithm (MMA) employing cost functions which depend on the different amplitude levels of the

constellation can be employed [56].


Figure 2.8: Adaptive MIMO equalizer structure.

2.4.5 Frequency Offset Compensation

Once synchronization between transmitter and receiver clocks is achieved, the received signal

remains impaired with phase noise. The remaining phase noise relates to the frequency difference

between the free running transmitting and local oscillator lasers (frequency offset) and the phase

noise coming from the non-spectral purity (laser phase noise) transmitter and LO lasers. In practice,

it is convenient to mitigate for these impairments separately [17]. The mitigation of the bulk

frequency offset in the first place improves the efficiency of the subsequent carrier phase recovery

as it reduces the amount of phase noise it needs to track. In addition, many carrier phase recovery

schemes are only unbiased in the presence of zero frequency offset. Non-data-aided frequency

offset estimation algorithms are preferred as the use of training symbols is not required in these

cases. Frequency offset algorithms can largely be divided into three categories [57]. The first

method uses the M-th power operation to remove the modulation component and extract the

residual frequency offset either in time domain differential phase based methods [58,59] or

frequency domain FFT-based methods [60,61,62]. The M-th power algorithm works well for M-

PSK modulated signals where the modulation can be removed with the M-th power operation.

However, for more general mQAM, the number of suitable symbols for the M-th power operation

decreases with the order of the constellation which decreases the performance of the algorithm.

The second method is based on the blind frequency search algorithm for arbitrary mQAM

constellations [57,63]. This method employs a number of test frequencies which are applied to the

received signal to evaluate a cost function. The frequency offset test minimizing the cost function

corresponds to the estimated frequency offset. The third method employs a starting training

sequence to get an initial frequency offset estimator [64]. Then, the recovered angle in the carrier

phase recovery is used to keep track of the frequency offset.

xyh

xxh

yxh

yyh

inx

iny

H H

out xx in xy inx h x h y

H H

out yx in yy iny h x h y


2.4.6 Carrier Phase Recovery

After frequency offset compensation, carrier phase recovery algorithms are employed to estimate

and compensate for the phase noise induced by the non-ideal transmitting and local oscillator lasers.

A more in-depth study of different carrier phase recovery schemes is performed in the following 3

and 4 chapters.

2.4.7 Symbol Estimation and Decoding

After carrier phase recovery, symbol estimation and symbol decoding are performed. This process

can be performed by a soft-decision forward error correction (FEC) module on the received

symbols. Alternatively, symbol estimation followed by hard-decision FEC can be employed. In

this case, for general square mQAM constellations and assuming to be limited by AWGN,

rectangular decision boundaries corresponding to the maximum likelihood symbol estimation can

be employed. However, in systems with relatively high phase noise, it is possible to improve the

performance by employing non-linear detection boundaries [66]. Furthermore, phase noise might

impact FEC performance as FEC codes are developed under the assumption of AWGN channels.

21

Chapter 3

CPR Schemes for Phase Noise Tolerant

Circular mQAM Formats

High spectral efficient modulations have the potential to increase the transmission capacity in

coherent optical communications at no cost in bandwidth requirements. However, as the

modulation order increases, the requirements on the performance of carrier phase recovery

schemes become stricter and their design more complicated. In this chapter, we study the

advantages of employing high order circular mQAM (C-mQAM) against conventional square

mQAM in terms of phase noise tolerance. The implementation complexity of suitable, high phase

noise tolerant CPR schemes for these modulations is also discussed. In this chapter we discuss

Papers I-IV.

3.1 Phase Noise Tolerant C-mQAM

High spectral efficient modulation formats are a promising solution to increase the capacity in

coherent optical communication systems as more information can be encoded per transmitted

symbol. Thus, the use of high order modulation formats comes at no extra bandwidth requirements.

However, the tolerance of these high order modulation formats against different transmission

impairments such as AWGN and laser phase noise is reduced as their constellation points are

inherently closer in the complex plane. Therefore, the requirements on the performance of the

algorithms used to mitigate different signal generation, transmission and reception impairments

are stricter. On the other hand, for the phase noise impairment case, the design of high phase noise

tolerant CPR schemes suitable for high order modulations becomes more difficult. Different feed-

back and feed-forward CPR schemes have been traditionally employed for carrier phase estimation

and compensation. Feedback CPR structures provide poorer phase noise tolerance due to the long

required feedback delay [18]. The processing speed of the ASICs in which CPR schemes are

implemented is typically much less than the baud rates employed in current coherent transmission

22 CHAPTER 3. CPR SCHEMES FOR PHASE NOISE TOLERANT…

systems [67]. This means that the data processing, for a real time ASIC implementation, must be

performed by means of massive parallelization and pipelining. Parallelization refers to data

processing in several replicated modules at the same time. Pipelining consists in breaking the

structure of an algorithm in different steps and sequentially performing each of them at every clock

cycle. Therefore, the parallelization and pipelining required to perform CPR on the incoming high

baud rate signal creates a long feedback delay for feedback based CPR schemes which hinders its

phase noise tolerance. In practice, blind feedforward structures are often preferred due to its higher

phase noise tolerance and the possibility to accurately estimate the phase without the need of

training symbols [18,19,65]. Two blind feedforward CPR approaches are traditionally employed

for CPR which mainly rely on the M-th power operation employed in the Viterbi-Viterbi algorithm

or on the blind phase search algorithm:

Viterbi and Viterbi (V&V) algorithm:

The Viterbi and Viterbi algorithm employs the uniform angular distribution characteristic of m-

PSK constellations [22]. The modulation component in these constellations can be removed

employing the non-linear M-th power operation on the received symbols. The V&V operation

principle for CPR is illustrated in Figure 3.1. In order to perform the V&V algorithm for CPR, a

block of received symbols is firstly considered. The modulation component of the received

symbols within the block is then removed by the M-th power operation. The sum of 2N+1 symbols

is then considered to average the impact of AWGN followed by angle calculation and division by

M. The calculated phase noise estimator is then unwrapped in order to reduce cycle slip occurrence.

Cycle slips might occur due to AWGN-induced unwrap events causing rotations of the

constellation [19]. The final phase noise estimator is used to compensate for the phase noise of the

original symbol in the middle of the block.

Figure 3.1: Viterbi and Viterbi block diagram for carrier phase recovery.

Symbol Block

(2N+1) 1ˆ ˆk kunwrap

M

Delay

ˆkje

x k

x k

x̂ k

ˆ argN

M

k k n

n N

x

CHAPTER 3. CPR SCHEMES FOR PHASE NOISE TOLERANT … 23

Figure 3.2: Blind phase search block diagram for carrier phase recovery.

Blind phase search algorithm:

The operation principle of the blind phase search algorithm is illustrated in Figure 3.2 [18]. First,

a 2N+1 block of consecutive received symbols are considered for CPR. The block of received

symbols is rotated by a number of test phases B and fed into a decision circuit module. The decision

circuit module defines the closest constellation points in the ideal constellation for all symbols in

the block and for each of the rotated blocks. The squared distances of the 2M+1 symbols to its

closest constellation points in the original constellation are calculated for each of the rotated block

of symbols. Then, the sum of 2M+1 squared distances to the ideal constellation points, for all the

rotated blocks, is calculated for AWGN averaging and considered to be the BPS metric distance.

The test phase providing the minimum BPS metric distance is considered to be the phase noise

estimator for the symbol in the middle of the block. The phase noise estimator is then unwrapped

to reduce cycle slip occurrence and used to compensate for the phase noise of the original symbols.

The V&V algorithm for CPR cannot directly be employed in high order mQAM constellations

(m≥16) as the angular modulation component of all constellation points, for these cases, is not

uniformly distributed. Different algorithms have been proposed to adapt the V&V algorithm for

high order mQAM constellations based on a QPSK partitioning approach [23-25][68-72]. An

amplitude symbol module classification (partitioning) is firstly employed to isolate the mQAM

constellation points belonging to QPSK angular positions. The QPSK partitioned symbols are then

employed for phase noise estimation in the V&V algorithm. However, since the symbols in high

order mQAM constellations have different amplitudes, it is convenient to normalize the partitioned

symbols prior to the M-th power operation. The normalization operation ensures that all symbols

inside the considered block contribute equally in the phase noise estimation process [23].

Symbol Block

(2M+1)

4ˆ

4

junw

rap

x k

Dis

tan

ce

calc

ula

tio

n

ije

Dec

isio

n

Cir

cuit

2

,

M

ik

ni

nM

Dd

min

ii

jD

x̂ k

0.... 1ii

i BB

fje

Delay x k

24 CHAPTER 3. CPR SCHEMES FOR PHASE NOISE TOLERANT…

1ˆ unwrap arg

M

Nk n

kn N

k n

x

M x

(3.1)

The small percentage of constellation points suitable for CPR in the V&V method limits the phase

noise tolerance of this algorithm when applied to high order mQAM constellations. Moreover, the

partitioning process is a less efficient process for low OSNR values and/or high order

constellations which again, limits the performance of the algorithm.

The BPS algorithm, on the other hand, provides good phase noise tolerance and scalability to high

order constellations as all constellation points can be employed for phase noise estimation.

However, the enhanced phase noise tolerance comes at the expense of a large implementation

complexity of the algorithm [71-73]. The number of required test phases to achieve high phase

noise tolerance largely increases with the modulation order creating a burden for its real

implementation. The reduction of the BPS implementation complexity, such as employing

different BPS distance metric calculations or reducing the number of required test phases, is under

extensive research [73,74]. Multi-stage CPR algorithms employing different approaches for each

of the stages have been proposed and shown to relax the implementation complexity of the overall

CPR scheme while maintaining a high phase noise tolerance [68-75]. However, the resulting multi-

stage CPR schemes still show a considerable high implementation complexity. This is especially

important for industrial applications as the trend is to transition towards pluggable transceivers

where power dissipation becomes critical.

A different alternative approach to achieve high phase noise tolerance at low c

phase noise tolerant modulation formats and dsp...

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